The Conservative group at East Devon District Council has expressed its disappointment over the closure of Seaton Jurassic.
The visitor attraction closed after five years in September, as Devon Wildlife Trust chose not to renew its contract to manage the centre, having seen a significant drop in visitor numbers during the pandemic.
The building is also suffering from a number of defects that could cost up to £200,000 to fix.
The council-owned centre will now remain closed until a decision can be made on the future of the site by East Devon District Council's Cabinet next year, with options including redesigning Seaton Jurassic, selling the building or using it as a different type of attraction.
But Conservative members of the council have now released a statement saying they hope it will remain in its original use.
The statement said: "It is difficult to see how an attraction designed around the story of rocks and time can be repurposed for something else, an idea being floated by the current administration at EDDC.
"There is no evidence that a change of style would work and continue to draw visitors to Seaton, as was the case previously.
"The Seaton Jurassic Centre has still to reach its full potential in telling the story of our planet’s past, especially in educating us on its constantly changing climate with or without human interference.
"Geologists will tell you, the key to understanding the future is written in the past."
The Conservatives are now calling on the leadership at EDDC to "stop indulging in a pointless blame game to get them out of this current mess, and look to the future".
The comments come after council leader Paul Arnott said he administration had "inherited this sad state of affairs".
The Conservative group's statement continued: "They should be setting their sights on making this well-loved attraction the success it deserves to be, rather than walking away from the various legacy and educational benefits this site offers.
"Paul Arnott, leader of EDDC, yet again imposes his personal opinions on the residents of Seaton and East Devon, promising to look back rather than forward.
"He fails to mention the number of awards this important place has been honoured with. Instead he chooses to blame its initial cost and design on alleged flawed judgement by the previous leadership rather than COVID and all the restrictions that has brought."
Leader of the EDDC Conservative group, Colin Brown, said: “Cllr Paul Arnott has performed a gross disservice to the people of Seaton who gave so much of their time to make the Seaton Jurassic centre work, without knowing the detail or the full facts.
"We strongly believe that with a different management style, even in its present form it can work.
"As the tourism and hospitality sector recovers from the worst ravages of the COVID-19 pandemic, Paul Arnott must take responsibility for the job he has right now, rather than yet again trying to shift the blame from a position that no one could have predicted pre the pandemic.
"It’s easy to criticise, but this is a time where solutions are required, not more negative thinking."
In his initial statement, Cllr Arnott did thank "the hundreds of volunteers who gave their time so generously to try and make a go of Seaton Jurassic".
He added: "I know many of them well and, long before I was a district councillor, they were openly sharing with me their concerns about both the viability and the construction of the building.
"My administration has inherited this sad state of affairs, but we will work tirelessly to make sure that the eventual outcome is a vast improvement on what exists, and out of respect for the thousands of free hours given by Seaton people doing their best we will make sure we find out and publish how this project was commissioned against the better judgement of so many people at the time."
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